Problem: Simplify the following expression: $\sqrt{18} + \sqrt{50}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{18} + \sqrt{50}$ $= \sqrt{9 \cdot 2} + \sqrt{25 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{2} + \sqrt{25} \cdot \sqrt{2}$ $= 3\sqrt{2} + 5\sqrt{2}$ Finally, simplify by combining the terms. $= ( 3 + 5 )\sqrt{2} = 8\sqrt{2}$